Syllabus

Holding Period Returns and Arithmetic and Geometric Means

Holding Period Return:

The holding period return is the total return over a period, irrespective of the length of the period. A holding period return can be computed for a day, a week, a month, a quarter, a year, a decade, or a century, or any fraction of the above possibilities. It is simply the total return you earn over a period of time. For example, if you invested $100 today, and in 2.37 years you have $128.49(assuming you do not receive any income in between), then your holding period return is:

Holding period return=Ending Value+Income-Beginning ValueBeginning Value

$128.49+0-$100$100-1=28.49%

So the holding period return on your investment over the 2.37 years is 28.49%.

The income in the equation can be interest on an account, dividends on a stock, or interest on a bond. The equation can be used for any investment that has an ending value, a beginning value and generates or does not generate income.

Arithmetic Mean:

The arithmetic mean is the simple average of a return series over time. It is commonly used in many facets of everyday life, and it is easily understood and calculated. The arithmetic mean is achieved by adding all values and dividing by the number of values (n). For example, if a stock has observed the following returns:

Year | Return |

2008 | 3% |

2009 | 5% |

2010 | 8% |

2011 | -1% |

2012 | 10% |

Then its arithmetic mean is:

AM=3%+5%+8%-1%+10%5=25%5=5.00%

This is easily accomplished using simple math, but the average return fails to take into account compounding.

Geometric Mean:

The geometric mean, sometimes referred to as compounded annual growth rate or time-weighted rate of return, is the average rate of return of a set of values calculated using the products of the terms. What does that mean? Geometric mean takes several values and multiplies them together and sets them to the 1/nth power. Geometric mean is an important tool for calculating portfolio...